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Effects of (Small) Permanent Charge and Channel Geometry on Ionic Flows via Classical Poisson--Nernst--Planck Models
Ji, Shuguan Liu, Weishi Zhang, Mingji
Ji, Shuguan
Liu, Weishi
Zhang, Mingji
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Abstract
In this work, we examine effects of permanent charges on ionic flows through ion channels via a quasi-one-dimensional classical Poisson--Nernst--Planck (PNP) model. The geometry of the three-dimensional channel is presented in this model to a certain extent, which is crucial for the study in this paper. Two ion species, one positively charged and one negatively charged, are considered with a simple profile of permanent charges: zeros at the two end regions and a constant $Q_0$ over the middle region. The classical PNP model can be viewed as a boundary value problem (BVP) of a singularly perturbed system. The singular orbit of the BVP depends on $Q_0$ in a regular way. Assuming $|Q_0|$ is small, a regular perturbation analysis is carried out for the singular orbit. Our analysis indicates that effects of permanent charges depend on a rich interplay between boundary conditions and the channel geometry. Furthermore, interesting common features are revealed: for $Q_0=0$, only an average quantity of the channel geometry plays a role; however, for $Q_0\neq 0$, details of the channel geometry matter; in particular, to optimize effects of a permanent charge, the channel should have a short and narrow neck within which the permanent charge is confined. The latter is consistent with structures of typical ion channels.
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2015-01-15
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Society for Industrial and Applied Mathematics
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Liu_2015.pdf
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Ji, S., Liu, W., & Zhang, M. (2015). Effects of (Small) Permanent Charge and Channel Geometry on Ionic Flows via Classical Poisson--Nernst--Planck Models. SIAM Journal on Applied Mathematics, 75(1), 114-135.